
where the black blobs stand for the normalization factors \(1/\sqrt{d_A}\)  and \(1/\sqrt{d_B}\) , respectively.
The Hayden-Preskill thought experiment asks whether an input quantum state on \(\mathcal {H}_A\)  can be retrieved from the quantum information available on \(\mathcal {H}_{B^{\prime }}\)  and \(\mathcal {H}_D\) .
It was argued that, provided the quantum evolution \(U_{AB}\)  is a Haar random unitary operator, the retrieval is possible if \(N_D\ge N_A +\epsilon \)  for \(N_A\log d_A\) , \(N_D\log d_D\) , and some small positive number \(\epsilon \)  [1]}.
In this section, we review the recovery protocol and its relation to the information scrambling.
In this work, we do not set \(U_{AB}\)  to be a Haar random unitary operator but let it be a general unitary operator unless otherwise stated.
